Find the angle between the diagonal of a cube of side length 8 and the diagonal of one of its faces, so that the two diagonals have a common vertex. The angle should be measured in radians. (Hint: we may assume that the cube is in the first octant, the origin is one of its vertices, and both diagonals start at the origin.)

Answer:

The structure is shown below.

Explanation:

The formal charge (FC) is the charge that is more close to the actual charge in the real molecules and ions. It can be calculated based on the number of valence electrons (V), the shared electrons (S) and the electrons in the lone pairs (L) by the equation:

FC = V - (L + S/2)

Sulfur is in group 16 of the periodic table, so it has 6 valence electrons, and chlorine is from group 17 of the periodic table, and so it has 7 valence electrons. Chlorine can share only one electron, so it is stable. Sulfur can expand its octet (because it's from the third period) and can have more than 8 electrons when stable.

The possible formulas, from the empiric one, are:

SCl, S₂Cl₂, and S₃Cl₃.

To have FC = 0, chlorine must done only one bond, because S = 2, and L = 6, so:

FC = 7 - (6 + 2/2) = 0

So, it can not be the central atom of a structure. In the SCl, it will hav only a simple bond, so for sulfur, S = 2, and L = 4 (only the lone pairs are counted)

FC = 6 - (4+ 2/2) = +1

For S₂Cl₂, the two sulfurs must be bonded to a simple bond, and each one to one chlorine, thus, for both od them S = 4, and L = 4. so

FC = 6 - (4 + 4/2) = 0

So, it is the correct structure. The lewis structure represents the bonds by lines and the lone pairs of electrons by dots, and it is shown below.

Final answer:

The molecular formula for the compound formed when molten sulfur reacts with chlorine gas is [tex]S_2Cl_2[/tex], known as sulfur monochloride. Its Lewis structure shows two sulfur atoms, each bonded to a chlorine atom and to each other, with no formal charges.

Explanation:

When molten sulfur reacts with chlorine gas, the resulting compound with an empirical formula of SCl is sulfur monochloride. However, the molecular formula for sulfur monochloride is [tex]S_2Cl_2[/tex], since each molecule contains two sulfur atoms and two chlorine atoms. To draw its Lewis structure, we place the two sulfur atoms at the center, bonded to each other, and each sulfur atom has a single bond to a chlorine atom. Each sulfur atom needs to complete its octet by sharing one pair of electrons with chlorine and two pairs with another sulfur atom, resulting in a S-S single bond and S-Cl single bond for each sulfur. Since every atom needs to have a formal charge of zero, no charges are present in the Lewis structure. The Lewis structure will look like this:

Cl-S-S-Cl

Final answer:

The genome of an organism contains all its genetic material necessary for life and reproduction. Genome size varies widely across species and can inform us about genetic diversity and evolutionary history. The Human Genome Project and similar research have deepened our understanding of genomes and their role in growth, development, and evolution.

Explanation:

The genome of an organism includes all of its genetic material, which contains the necessary information for sustaining life and reproduction. As the complexity of organisms increases, generally, so does the size of their genomes. However, genome size doesn't correlate directly to the number of genes an organism has.

For instance, humans have about 3.5 pg of DNA in their genome, which translates to roughly 3.4 billion base pairs, despite not having the largest genome when compared to certain plants or even other animals. Intriguingly, a significant portion of the genome consists of non-coding DNA that doesn't seem to have a direct function in gene encoding.

Genome size differs widely across species, with eukaryotes often having multiple chromosomes and bacteria generally having smaller genomes. The genome size can provide information on an organism's genetic diversity and evolutionary history. The role of the genome is vital in the growth and development of organisms, dictating the specific instructions for these processes.

Additionally, the sequencing of genomes, as in the Human Genome Project, has provided valuable insights into genetic variations between and within species, fostering a greater understanding of evolutionary biology and potential medical advancements.

Answer:

238,485 Joules

Explanation:

The amount of energy required is a summation of heat of fusion, capacity and vaporization.

Q = mLf + mC∆T + mLv = m(Lf + C∆T + Lv)

m (mass of water) = 75 g

Lf (specific latent heat of fusion of water) = 336 J/g

C (specific heat capacity of water) = 4.2 J/g°C

∆T = T2 - T1 = 119 - (-20) = 119+20 = 139°C

Lv (specific latent heat of vaporization of water) = 2,260 J/g

Q = 75(336 + 4.2×139 + 2260) = 75(336 + 583.8 + 2260) = 75(3179.8) = 238,485 J

Answer:

(b)>(c)>(a) >(d)

Explanation:

We  know that from Rydberg´s equation:

1/ λ = Rh x (1/n₁² - 1/n₂² )

where n₁ and n₂ are the principal quantum numbers involved in the transition, and n₁ < n₂.

Therefore the wavelength will be given by taking the reciprocal of this equation:

λ  = 1 / [Rh x  (1/n₁² - 1/n₂² ) ]

So lets calculate the wavelengths for the transitions in this question expressed in terms of the constant Rh

(a ) λ  = 1 / [Rh x  (1/2² ) ] =  4/ Rh

(b ) λ  = 1 / [Rh x  (1/4² - 1/20² ) ] = 16.7 / Rh

(c)  λ  = 1 /  [Rh x  (1/3² - 1/10² ) ] = 9.9 / Rh

(d) λ  = 1  /  [Rh x  (1/1² - 1/2² ) ] =  1.33 / Rh

Therefore in decreasing wavelength is (b)>(c)>(a) >(d)

as shown in these calculations, be careful with this type of question, since one might erroneously think that the transition for example as in (a) will have a shorter wavelength than (d) which is not the case as shown here. One must use Rydbergs formula.

Arranging the H atom electron transitions in decreasing order ;  

B ---> C ----> A -----> D

Determine the wavelength of the photon absorbed by the H atom electron

we will apply Rydberg's equation

Rydberg equation =   1/ λ = Rh * (1/n₁² - 1/n₂² ) --- ( 1 )

n = quantum numbers

λ = wavelength

∴ λ  = 1 / [Rh * (1/n₁² - 1/n₂² ) ]  ---- ( 2 )

a) For n = 2 to n = [infinity]

λ = 1 / [ Rh * ( 1 / 2² - ∞ ) =  4 / Rh

b) For n = 4 to n= 20

λ = 1 / [ Rh * ( 1 / 4² - 1 / 20² ) = 16.7 Rh  ( highest wavelength )

c) For n = 3 to n = 10

λ  = 1 / [ Rh * ( 1 / 3² - 1 / 10² ) = 9.9 Rh

d) For n = 2 to n = 1

λ = 1 / [ Rh * ( 1 / 2² - 1 / 1² ) = 1.33 Rh  ( Lowest wavelength )

Therefore arranging the  H atom electron transitions in order of decreasing wavelength will be;  B ---> C ----> A -----> D.

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Answer:

F

Explanation:

simple subtration

In the manufacture of nitric acid by the oxidation of ammonia, the first product is nitric oxide. The nitric oxide is then oxidized to nitrogen dioxide. The standard reaction enthalpy for the reaction is −114.1 kJ/mol rxn.

A thermodynamic system's enthalpy is the sum of its internal energy and the product of its pressure and volume. It is a constant-pressure state function that is used in many measurements in chemical, biological, and physical systems.

Enthalpy is significant because it tells us how much heat is present in a system (energy). Heat is important because it allows us to generate valuable work. An enthalpy shift indicates how much enthalpy was lost or gained during a chemical reaction, with enthalpy referring to the heat energy of the system.

During chemical reactions, atom bonds can dissolve, reform, or both in order to absorb or release energy. The heat absorbed or emitted by a device under constant pressure is referred to as enthalpy.

Thus, option F is correct.

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The bromination of trans-stilbene results in meso-1,2-dibromo-1,2-diphenylethane, an achiral molecule. In contrast, the bromination of cis-stilbene yields enantiomeric products, (1R,2S)-1,2-dibromo-1,2-diphenylethane and (1S,2R)-1,2-dibromo-1,2-diphenylethane.

The bromination of trans-stilbene and cis-stilbene leads to different products due to the arrangement of the double bonds in the starting materials.

1. **Trans-Stilbene:**

  - In trans-stilbene, the two phenyl rings are on opposite sides of the double bond. Bromination in the presence of bromine ([tex]\(Br_2\)[/tex]) or other brominating agents typically occurs with syn-addition across the double bond.

  - The product is meso-1,2-dibromo-1,2-diphenylethane. The meso compound has a plane of symmetry, resulting in an achiral molecule.

2. **Cis-Stilbene:**

  - In cis-stilbene, the two phenyl rings are on the same side of the double bond. Bromination of cis-stilbene can yield two enantiomeric products due to anti-addition across the double bond.

  - The products are (1R,2S)-1,2-dibromo-1,2-diphenylethane and (1S,2R)-1,2-dibromo-1,2-diphenylethane.

Answer:

Explanation:

A >1000 °C does not conduct electricity : covalent ( usually do not conduct electricity, they are formed by the sharing of electrons)

B 850 °C conducts electricity in the liquid state, but not in the solid state: Ionic ( ionic or electrovalent compounds are formed between atoms where one loses an electron while the other gains e.g NaCl, they conduct electricity when dissolved in a polar solvent because they dissociate into ions and have high melting and boiling points)

750 °C conducts electricity in the solid state : Metallic ( metals generally have delocalized electrons that enables them to conduct electron since they are no associated with bond and are therefore free to move)

D 150 °C does not conduct electricity : Molecular ( consist mainly of molecules; they do not have charge)

Answer:

The molecules are hybridized at different angles as shown in the explanation.

Explanation:

The hybridization and the geometries of the carbon atoms are as follows:

C1     → sp², trigonal planar, angle = 120⁰

C (II)→  sp³, tetrahedral, angle = 109.5⁰

C(III)→ sp², trigonal planar, 120⁰

C(IV)→ sp³, trigonal pyramidal, 109, 5⁰

Answer:

C

Explanation:

The aqueous solution C has three ions where as b 2 ions and A no Ionization

Answer:

The formula is Be(NO3)2*3H2O. The number of waters in the hydrate is 3

Explanation:

Step 1: Data given

Mass of the hydrate sample = 3.41 grams

Mass after heating = 2.43 grams

Step 2: Calculate mass of water

After heating, all the water is gone. So the mass of water can be calculated by

Mass of hydrate before heating - mass after heating

Mass of water = 3.41 -2.43 = 0.98 grams

Step 2 : Calculate moles H2O

Moles H2O = mass H2O / molar mass H2O

Moles H2O = 0.98 grams / 18.02 g/mol

Moles H2O = 0.054 moles

Step 3: Calculate moles Be(NO3)2

Moles Be(NO3)2 = 2.43 grams / 133.02

Moles Be(NO3)2 = 0.0183 moles

Step 4: Calculate molecules water

Molecules H2O = 0.054 moles / 0.0183 moles

Molecules H2O = 3.0

The formula is Be(NO3)2*3H2O. The number of waters in the hydrate is 3

The number of waters of hydration in the hydrate is 3.

Based on the given information,  

• The formula of the beryllium nitrate hydrate is Be(NO3)2⋅xH2O.  

• The weight of the sample is 3.41 grams.

• The weight of the sample after heating of the sample is 2.43 grams {weight of Be(NO3)2}.  

Now, the mass of xH2O will be,  

= 3.41 g - 2.43 g  

= 0.98 grams

The moles of Be(NO3)2 will be calculated as,  

Mass of Be(NO3)2/Molecular weight of Be(NO3)2 = 2.43 g/133 = 0.01827 moles

The moles of xH2O = 0.98/18 = 0.05444 moles

Now the value of x will be,  

= 0.05444/0.01827  

= 3

Thus, the number of waters of hydration in the hydrate is 3.

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Answer:

Electromagnetic waves are usually defined as those waves that are generated due to the vibrations between an electric as well as a magnetic field. Here, the component comprising the electric field and the component comprising the magnetic field vibrates perpendicular to each other, and both are in phase. Some of the examples of this type of wave are microwaves, infrared, ultra-violet, visible light, X-rays and many more.

The microwave and ultraviolet radiations are two electromagnetic waves that have similar characteristics, travel at a similar speed of about 300,000 km per second.

They differ from one another in many ways. It is because the microwaves have a higher wavelength, low frequency, and low energy. On the other hand, ultraviolet radiations have a low wavelength, high frequency, and high energy.

Answer:

[tex]7.3\times 10^2\ days[/tex]

Explanation:

Given that:

Half life = [tex]9.8\times 10^3[/tex] days

[tex]t_{1/2}=\frac{\ln2}{k}[/tex]

Where, k is rate constant

So,  

[tex]k=\frac{\ln2}{t_{1/2}}[/tex]

[tex]k=\frac{\ln2}{9.8\times 10^3}\ days^{-1}[/tex]

The rate constant, k = 0.00007 days⁻¹

Using integrated rate law for first order kinetics as:

[tex][A_t]=[A_0]e^{-kt}[/tex]

Where,  

[tex][A_t][/tex] is the concentration at time t

[tex][A_0][/tex] is the initial concentration

Given:

5 % is lost which means that 0.05 of [tex][A_0][/tex] is decomposed. So,

[tex]\frac {[A_t]}{[A_0]}[/tex] = 1 - 0.05 = 0.95

t = ?

[tex]\frac {[A_t]}{[A_0]}=e^{-k\times t}[/tex]

[tex]0.95=e^{-0.00007\times t}[/tex]

t = 732.76 days = [tex]7.3\times 10^2\ days[/tex]

It will take approximately [tex]\( 7.25 \times 10^2 \)[/tex] days for benzoyl peroxide to lose 5% of its potency when refrigerated.

To determine the time, it takes for benzoyl peroxide to lose 5% of its potency, we can use the first-order reaction kinetics formula:

[tex]\[ N(t) = N_0 \times e^{-kt} \][/tex]

where:

[tex]\( N(t) \)[/tex] is the amount of substance remaining after time [tex]\( t \)[/tex],

[tex]\( N_0 \)[/tex] is the initial amount of substance,

[tex]\( k \)[/tex] is the rate constant,

[tex]\( t \)[/tex] is the time.

The half-life [tex]\( t_{1/2} \)[/tex] is related to the rate constant [tex]\( k \)[/tex] by the equation:

[tex]\[ t_{1/2} = \frac{\ln(2)}{k} \][/tex]

Given the half-life [tex]\( t_{1/2} = 9.8 \times 10^3 \)[/tex] days, we can solve for [tex]\( k \)[/tex]:

[tex]\[ k = \frac{\ln(2)}{t_{1/2}} = \frac{\ln(2)}{9.8 \times 10^3} \][/tex]

Now, we want to find the time [tex]\( t \)[/tex] when 95% of the substance remains, so [tex]\( N(t) = 0.95N_0 \)[/tex]. Plugging this into the first-order reaction formula:

[tex]\[ 0.95N_0 = N_0 \times e^{-kt} \][/tex]

[tex]\[ 0.95 = e^{-kt} \][/tex]

Taking the natural logarithm of both sides:

[tex]\[ \ln(0.95) = -kt \][/tex]

Solving for [tex]\( t \)[/tex]:

[tex]\[ t = -\frac{\ln(0.95)}{k} \][/tex]

Substituting [tex]\( k \)[/tex] with the expression involving the half-life:

[tex]\[ t = -\frac{\ln(0.95)}{\ln(2)/t_{1/2}} \][/tex]

[tex]\[ t = -\frac{\ln(0.95) \cdot t_{1/2}}{\ln(2)} \][/tex]

[tex]\[ t = -\frac{\ln(0.95) \cdot 9.8 \times 10^3}{\ln(2)} \][/tex]

[tex]\[ t \approx -\frac{\ln(0.95) \cdot 9.8 \times 10^3}{0.693} \][/tex]

[tex]\[ t \approx -\frac{-0.051293 \cdot 9.8 \times 10^3}{0.693} \][/tex]

[tex]\[ t \approx \frac{0.5027 \times 10^3}{0.693} \][/tex]

[tex]\[ t \approx 7.25 \times 10^2 \][/tex]

Answer:CCl3CO2H

Explanation:

CCl3CO2H is the strongest among the list because it ionize to give all its hydrogen ion

CCl3CO2H <==> H+ + CCL3COO-

CCl3CO2H has the largest acid equilibrium constant, Ka, because it contains the most Cl atoms per molecule, which enhances its ability to donate protons.

The equilibrium constant Ka in acid-base chemistry is the acid dissociation constant. It represents the extent to which a compound donates protons (H+) in a solution. A larger Ka value indicates a stronger acid. When we compare CH3CO2H, CH2ClCO2H, CHCl2CO2H, and CCl3CO2H, the acid with the most Cl atoms has the largest Ka because Cl is a highly electronegative atom. This electronegativity pulls electron density away from the acidic H atom, making it easier to lose, which means the acid is stronger. So, CCl3CO2H has the largest acid equilibrium constant, Ka.

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Answer:

0.76

Explanation:

N = No(0.5)^t/t1/2

N/No = (0.5)^t/t1/2

t = 2300 years, t1/2 = 5730 years

N/No = (0.5)^2300/5730 = 0.5^0.401 = 0.76

Answer:HCl(aq) + NaOH (aq) -> NaCl (aq) + H2O(l)

Explanation:

The reaction of HCl and NaOH is a neutralization reaction. When an acid and a base react salt and water is produced.

HCl(aq) + NaOH (aq) ----> NaCl (aq) + H2O(l)

Because the reactants and products are ionic compounds, they exist as ions in a solution.

H+(aq) + Cl-(aq) + Na+(aq) + OH-(aq) -------> Na+(aq) + Cl-(aq) + H2O(l)

The aim of a neutralization reaction is the formation of water. Na+(aq) + Cl-(aq) remain the same on both the reactants side and the products side, the net ionic reaction will be

H+(aq) + OH-(aq) -------> H2O(l)

The reaction of HCl and NaOH forms water in a neutralization reaction. The net ionic equation, H⁺ + OH⁻ → H₂O, emphasizes the essential combination of ions to produce water.

The reaction between hydrochloric acid (HCl) and sodium hydroxide (NaOH) is a neutralization reaction, resulting in the formation of water and salt. In molecular form, the equation is written as:

HCl(aq) + NaOH(aq) → NaCl(aq) + H₂O(l)

Considering the ionic nature of these compounds in solution, they exist as ions. The complete ionic equation includes the dissociation of each compound into its constituent ions:

H⁺(aq) + Cl⁻(aq) + Na⁺(aq) + OH⁻(aq) → Na⁺(aq) + Cl⁻(aq) + H₂O(l)

Sodium cations (Na⁺) and chloride anions (Cl⁻) remain unchanged on both sides, acting as spectator ions. Eliminating these spectator ions yields the net ionic equation:

H⁺(aq) + OH⁻(aq) → H₂O(l)

This simplified representation emphasizes the essential components of the neutralization reaction, focusing on the combination of hydrogen ions (H⁺) from the acid and hydroxide ions (OH⁻) from the base to form water. The net ionic equation succinctly captures the core chemical transformation occurring in the neutralization process.

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Answer:

what is the amount of energy ( Δ G ) required = 36.65KJ

Explanation:

The concept of VANT HOFF ISOTHERM EQUATION was used, as well as the relationship between the gibb's free energy and the electromotive force, all the steps and appropriate calculations is as shown in the attached file in order to get the amount of energy required for the transport of the hydrogen ions.

The energy required for the transport of hydrogen ions from a cell to the stomach lumen can be calculated using the Nernst equation and the equation for Gibbs free energy.

The amount of energy required for the transport of hydrogen ions from a cell into the stomach lumen can be calculated using the Nernst equation and the equation for Gibbs free energy. The Nernst equation relates the equilibrium potential for an ion to the concentrations of the ion on either side of the membrane, while the equation for Gibbs free energy relates the change in free energy to the change in potential across the membrane and the Faraday constant. By substituting the given values into these equations, the amount of energy required can be calculated.

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In an acid-base reaction, the Brønsted–Lowry acid donates a proton and becomes a conjugate base while the Brønsted–Lowry base accepts a proton and becomes a conjugate acid. The reactions given as examples illustrate these changes with H2CO3 and H2O acting as acids in the two reactions while H2O and NH3 act as bases respectively.

In the reaction, Brønsted–Lowry acid is the species that donates a proton (H+), and the Brønsted–Lowry base is the species that accepts a proton. After the acid has lost a proton, it becomes the conjugate base. Conversely, after the base gains a proton, it becomes the conjugate acid.

For the reaction H2CO3(aq) + H2O(l) ∆ H3O+(aq) + HCO3 -(aq), H2CO3 is the Brønsted-Lowry acid and H2O is the Brønsted-Lowry base. Upon losing a proton, H2CO3 becomes HCO3- which is the conjugate base and upon gaining a proton, H2O becomes H3O+ which is the conjugate acid.

For the reaction NH3(aq) + H2O(l) ∆ NH4 +(aq) + OH-(aq), NH3 is the Brønsted-Lowry base and H2O is the Brønsted-Lowry acid. Upon gaining a proton, NH3 becomes NH4+ which is the conjugate acid and upon losing a proton, H2O becomes OH- which is the conjugate base.

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In a Brønsted-Lowry reaction, the acid donates a proton and the base accepts the proton. The species formed when an acid donates a proton becomes a conjugate base, and the species formed when a base accepts a proton becomes a conjugate acid. In the given reactions, H2CO3 and H2O function as acids, and H2O and NH3 function as bases.

In a Brønsted-Lowry acid-base reaction, an acid is a substance that donates a proton (H+) and a base is a substance that accepts a proton. A conjugate acid is the species formed when a Brønsted-Lowry base gains a proton, and a conjugate base is the species remaining after a Brønsted-Lowry acid has lost a proton.

For the reaction H2CO3(aq) + H2O(l) ∆ H3O+(aq) + HCO3 -(aq), the Brønsted-Lowry acid is H2CO3, which donates a proton to become the conjugate base, HCO3-. The Brønsted-Lowry base is H2O, which accepts a proton to become the conjugate acid, H3O+.

For the reaction NH3(aq) + H2O(l) ∆ NH4 +(aq) + OH-(aq), the Brønsted-Lowry base is NH3, which accepts a proton to become the conjugate acid, NH4+. The Brønsted-Lowry acid is H2O, which donates a proton to become the conjugate base, OH-.

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Answer:

Explanation:

Calcium is the element of the group 2 and period 4 which means that the valence electronic configuration is [tex]1s^22s^22p^63s^23p^64s^2[/tex] or [tex][Ar]4s^2[/tex].

Chlorine is the element of the group 17 and period 3 which means that the valence electronic configuration is [tex]1s^22s^22p^63s^23p^5[/tex] or [tex][Ne]3s^23p^5[/tex].

Thus, calcium losses 2 electrons to 2 atoms of chlorine and these 2 atoms of chlorine accepts each electron to form ionic bond. This is done in order that the octet of the atoms are complete and they become stable.

Thus, the formula of calcium chloride is [tex]CaCl_2[/tex].

Hence, in [tex]CaCl_2[/tex], Calcium exits in [tex]Ca^{2+}[/tex] form which has electronic configuration of [tex]1s^22s^22p^63s^23p^6[/tex] or [tex][Ar][/tex]

The ground-state electron configuration for a calcium ion (Ca²+) is 1s²2s²2p63s²3p6, the same configuration as the noble gas Argon (Ar). This is because a calcium ion loses its two 4s valence electrons when it forms a cation.

The calcium ion, denoted as Ca²+, has lost its valence electrons to form a cation. In an uncharged, ground state calcium atom, it contains 20 electrons with configuration as 1s²2s²2p63s²3p64s². When it loses its two 4s valence electrons to become a cation, its electron configuration changes to 1s²2s²2p63s²3p6 which is similar to the noble gas Argon (Ar).

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Explanation:

Electron affinity of 7th group elements whose electron affinity of their anionic forms ( EA2) are higher than the electron affinity of their neutral form(EA1). This is because their anionic forms are more stable than their neutral form. If the reaction is endothermic ,change in the energy is negative this means that electron affinity is positive. And vice versa for negative electron affinity.

The EA2 of oxygen is positive because energy is required to add an electron to a small space that is already dense with negative charge. The EA2 of sulfur is also positive.

The electron affinity refers to the energy evolved when one mole of electrons is added to an atom. We know that the energy required to add the second electron to oxygen is positive rather than negative implying that the process is endothermic.

This is because, energy is required to add an electron to a small space that is already dense with negative charge. The EA2 of sulfur is also positive.

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Answer:

40mL of glycerol are needed to make a 20% v/v solution

Explanation:

This problem can be solved with a simple rule of three:

20%  v/v is a sort of concentration. In this case, 20 mL of solute are contained in 100 mL of solution.

Therefore, in 100 mL of solution you have 20 mL of solvent (glycerol)

In 200 mL, you would have,  (200 .20)/ 100 = 40 mL

Answer:

(a) ν = 3.1 × 10¹³ s⁻¹

(b) λ = 3.467 μm

Explanation:

We can solve both problems using the following expression.

c = λ × ν

where,

c: speed of light

λ: wavelength

ν: frequency

(a)

c = λ × ν

ν = c / λ

ν = (3.000 × 10⁸ m/s) / (9.6 × 10⁻⁶ m)

ν = 3.1 × 10¹³ s⁻¹

(b)

c = λ × ν

λ = c / ν

λ = (3.000 × 10⁸ m/s) / (8.652 × 10¹³ s⁻¹)

λ = 3.467 × 10⁻⁶ m

λ = 3.467 × 10⁻⁶ m (10⁶ μm/ 1 m)

λ = 3.467 μm

Answer:

The mass of CaCO3 reacted  is 5.00 grams

Explanation:

Step 1 :Data given

Before the reaction, the container, including the CaCO3, had a mass of 24.20 g

After the reaction the container with product had a mass of only 22.00 g because the CO2 gas produced did not remain in the container.

Molar mass of CO2 = 44.01 g/mol

Molar mass CaCO3 = 100.09 g/mol

Step 2: The balanced equation

CaCO3 → CaO + CO2

Step 3: Calculate mass of CO2

Mass of CO2 = 24.20 grams - 22.00 grams

Mass of CO2 = 2.20 grams

Step 4: Calculate moles CO2

Moles CO2 = mass CO2 / molar mass CO2

Moles CO2 = 2.20 grams / 44.01 g/mol

Moles CO2 = 0.0500 moles

Step 5: Calculate moles CaCO3

For 1 mol CaCO3 we'll have 1 mol CaO and 1 mol CO2

For 0.0500 moles CO2 we need 0.0500 moles CaCO3

Step 6: Calculate mass CaCO3

Mass CaCO3 = moles CaCO3 * molar mass CaCO3

Mass CaCO3 = 0.0500 moles  * 100.09 g/mol

Mass CaCO3 = 5.00 grams

The mass of CaCO3 reacted  is 5.00 grams

Final answer:

2.20 grams of calcium carbonate (CaCO3) reacted, as calculated by the difference in mass before and after the decomposition reaction, which released carbon dioxide gas from the container.

Explanation:

The initial mass of the reaction container with calcium carbonate (CaCO3) was 24.20 g, while the final mass after the reaction was 22.00 g. The mass of CaCO3 that reacted can be found by subtracting the final mass from the initial mass, because the only mass lost would be the carbon dioxide (CO2) gas that escaped from the container.

Mass of CaCO3 that reacted = Initial mass - Final mass
= 24.20 g - 22.00 g
= 2.20 g

Therefore, 2.20 grams of calcium carbonate reacted, decomposing into calcium oxide (CaO) and releasing carbon dioxide gas according to the reaction CaCO3(s) → CaO(s) + CO2(g).

Answer:

0.0634 M.

Explanation:

Equation of the neutralisation reaction:

CH3COOH + NaOH--> CH3COONa + H2O

Number of moles = molar concentration * volume

= 0.1002 * 0.01581

= 0.00158 mol.

By stoichiometry,

1 mole of acetic acid reacts with 1 mole of NaOH

Number of moles of acetic acid = 0.00158 mol.

Concentration in 2nd dilution = moles/ volume

= 0.00158/0.25

= 0.00634 M

At 25 ml,

Concentration =

C1 * V1 = C2 * V2

= (0.00634 * 0.25)/0.025

= 0.0634 M.

Given:

Neutralization reaction's equation:

Now,

The number of moles will be:

= [tex]Molar \ concentration\times Volume[/tex]

= [tex]0.1002\times 0.01581[/tex]

= [tex]0.00158 \ mol[/tex]

and,

The concentration of second dilution will be:

= [tex]\frac{Moles}{Volume}[/tex]

= [tex]\frac{0.00158}{0.25}[/tex]

= [tex]0.00634 \ M[/tex]

hence,

The concentration at 25 mL will be:

→ [tex]C_1\times V_1 = C_2\times V_2[/tex]

or,

→         [tex]C_2 = \frac{C_1\times V_1}{V_2}[/tex]

                 [tex]= \frac{0.00634\times 0.25}{0.025}[/tex]

                 [tex]= 0.0634 \ M[/tex]

Thus the above response is right.  

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Answer: Molarity of this solution is 0.88 M

Explanation:

Molarity : It is defined as the number of moles of solute present in one liter of solution.

Formula used :

[tex]Molarity=\frac{n\times 1000}{V_s}[/tex]

where,

Given : 3.0 g of hydrogen peroxide is present in 100 g of solution.

n = moles of solute = [tex]\frac{\text {given mass}}{\text {molar mass}}=\frac{3.0g}{34g/mol}=0.088mol[/tex]

[tex]V_s[/tex] = volume of solution in ml= [tex]\frac{\text {mass of solutuion}}{\text {density of solution}}=\frac{100g}{1.01g/ml}=99.0ml[/tex]

Now put all the given values in the formula of molarity, we get

[tex]Molarity=\frac{0.088moles\times 1000}{99.0ml}=0.88mole/L[/tex]

Thus molarity of this solution is 0.88 M

Answer:

1. Zn is oxidize.

Cu is reduced.

2. Fe is oxidize.

H2 is reduced.

Explanation:

1. Zn(s)+Cu2+(aq)→Zn2+(aq)+Cu(s)

From the equation,

Zn changes oxidation number from 0 to +2. Therefore Zn is oxidized.

Cu2+ changes oxidation number from +2 to 0. Therefore, Cu2+ is reduced

2. 3Fe(s)+4H2O(g)→Fe2O3(s)+4H2(g)

From the equation,

Fe changes oxidation number from 0 to +3. Therefore, Fe is oxidized.

H changes oxidation number from +1 to 0. Therefore, H is reduced

Answer:

a. alkyne

b. alkane

c. alkyne

d. alkene

Explanation:

The general formula for each class of compound is given below

Alkane: [tex]C_nH_{2n+2}[/tex]

Alkene: [tex]C_nH_{2n}[/tex]

Alkyne: [tex]C_nH_{2n-2}[/tex] (assuming single multiple bonds)

Now let us classify according to the above formulas:

a. It has two hydrogen atoms less than the two times of carbon atoms hence, it's alkyne

b. It has two hydrogen atoms more than the two times of carbon atoms hence, it's alkane

c. It has two hydrogen atoms less than the two times of carbon atoms hence, it's alkyne

d. It has hydrogen atoms two times of carbon atoms hence, it's alkene

Answer:Based on the molecular formula, the following compounds belongs to the following groups:

a. C6H10 ( alkyne)

b. C4H10 ( alkane)

c. C8H14 (alkyne)

d. C8H16 (alkene)

Explanation: Hydrocarbon is an organic chemical compound that contains Hydrogen and carbons. There are three main types of Hydrocarbons which includes:

- Saturated Hydrocarbons.( They are composed entirely of single bonds and are saturated with hydrogen.). They are the alkane.

- Unsaturated Hydrocarbons: They are composed of either a double or triple bonds. The double bonds are the alkene and the triple bonds are the alkynes.

- Aromatic Hydrocarbons: they contain an aromatic ring. Example is the Benzene.

I hope this helps. Thanks.

Answer:

The pH of the solution is 4.28

Explanation:

The dissolution reaction as below

CH₃COOH ⇔  CH₃COO⁻ + H⁺

[tex]K_{a} = \frac{[CH_{3}COO^{-}][H^{+}]}{[CH_{3}COOH} = 10^{-4.76}[/tex]

Assume the concentration of the ion, [H⁺] = a,

          so [CH₃COO⁻] = a and [CH₃COOH] = 3a

Then use the formula of Ka, we get

Ka = a * a / 3a = 10^-4.76 ⇔ a = 3 x 10^-4.76 = 5.21 x 10^-5

Hence pH = -log(a) = - log(5.21 x 10^-5) = 4.28

To calculate the price at which the bonds sold, we use the present value formula for bonds.

To calculate the price at which the bonds sold, we need to use the formula for present value of a bond. The formula is:

PV = (C * (1 - (1 + r)^-n) / r) + (FV / (1 + r)^n)

Where PV is the present value, C is the coupon payment, r is the market yield, n is the number of periods, and FV is the face value.

In this case, the coupon payment is $2,010,000 (6% of $67 million). The market yield is 6%, the number of periods is 30 (15 years * 2 semiannual payments per year), and the face value is $67 million. Plugging these values into the formula, we get:

PV = (2,010,000 * (1 - (1 + 0.06)^-30) / 0.06) + (67,000,000 / (1 + 0.06)^30)

Calculating this expression will give us the price at which the bonds sold.

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Answer:

5.48 g

Explanation:

The concentration in M represents the mol/L, or the number of moles in each L of the solution, and it can be calculated by the number of moles (n) divided by the volume of the solution (V) in L, so:

M = n/V

1.71 = n/0.100

n = 0.171 mol

The molar mass of methanol is 32.04 g/mol, and it is the mass (m) divided by the number of moles:

FM = m/n

32.04 = m/0.171

m = 5.48 g

Answer:

The question has some part missing which I have added in the attachment.

Explanation:

The reactions given occur under certain reagents, which we are told to pick for each of the reaction synthesis. Conventionally, halogens have the ability to undergo addition reactions with hydrocarbons by breaking down the double or triple bond in them to a single bond, this usually occur by electron donation and electron acceptor.

The attachment shows the reactions and the necessary reagents required for each